I lost weight with just walking. I didn't go to the gym. Did the odd yoga class.
I have regular DEXA scans and I lost very little muscle, like 3 pounds, which the Dr told me was normal just because you don't need as much muscle to carry less weight around.
I kept my protein over 100 grams a day though, if you are living off 60 grams of protein and not working out, you are going to lose muscle.
If you just want to drop weight fast, you drop weight faster not exercising. There are a lot of studies on the lack of effectiveness of exercise for weight loss. Google and do your own research.